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On the behavior of quasi-local mass at the infinity along nearly round surfaces

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Abstract

In this article, we study the limiting behavior of the Brown–York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show that the ADM mass of an asymptotically flat three manifold can be approximated by some geometric invariants of a family of nearly round surfaces, which approach to infinity of the manifold.

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Authors and Affiliations

  1. Key Laboratory of Pure and Applied mathematics, School of Mathematics Science, Peking University, Beijing, 100871, People’s Republic of China

    Yuguang Shi & Jie Wu

  2. Faculty of Mathematics, University Magdeburg, 39016, Magdebrug, Germany

    Guofang Wang

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  1. Yuguang Shi
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  2. Guofang Wang
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  3. Jie Wu
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Correspondence to Yuguang Shi.

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Shi, Y., Wang, G. & Wu, J. On the behavior of quasi-local mass at the infinity along nearly round surfaces. Ann Glob Anal Geom 36, 419–441 (2009). https://doi.org/10.1007/s10455-009-9169-5

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  • DOI: https://doi.org/10.1007/s10455-009-9169-5

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